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On Measurement Uncertainties Derived from "Metrological Statistics"

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As measurement uncertainties are closely tied up with error models, it might be of interest to review a model, which the author assigns to Metrological Statistics. Given that the random errors are normally distributed, the experimentalist could either refer to B.L. Welchs concept of effective degrees of freedom or to the multidimensional Fisher-Wishart distribution density. In the first case, different numbers of repeated measurements are admissible, in the latter it is strictly required to have equal numbers of repeated measurements. In error propagation, however, only the latter mode of action opens up the possibility of designing confidence intervals according to Student and confidence ellipsoids according to Hotelling. Another point of view, closely linked to the choice of the numbers of repeated measurements, refers to the customary practice of attributing equal rights to statistical expectations and empirical estimators. However, the Fisher-Wishart distribution density suggests using only the information which is realistically accessible to experimentalists, namely empirical estimators. For the handling of unknown systematic errors, either the existence of a rectangular distribution density may be assumed or, and this is proposed here, they may be classified as time-constant quantities, biasing expectations and suspending a lot of tools and procedures of error calculus well-established otherwise.

Subject Categories:

  • Numerical Mathematics
  • Test Facilities, Equipment and Methods
  • Statistics and Probability

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